Field theoretic renormalization group in a model of anisotropic growth of an interface

Abstract

We study effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is described by theWolf model—anisotropic generalisation of Kardar—Parisi—Zhang model. The turbulent advecting velocity field is modelled by the anisotropic Avellaneda—Majda ensemble. Gaussian statistics with the correlation function vv ∝ δ(t − t )δ(k ) k −d+1−ξ ⊥ , where k is the wave number and 0 < ξ < 2 is a free parameter. Using the field theoretic renormalization group we establish existence of the fixed points both for the model without advection and for the model with it — in the former case the results are in a good adreement with those of Wolf. It turns out that in the case of spacial dimension d = 2, all found fixed points converge to one — a Gaussian point; nevertheless, this does not forbid the existence of the physical “non-perturbative” strong-coupling fixed point of Kardar—Parisi— Zhang model which can survive in our model. Addition of the velocity field destroys stability of the fixed points and forbids “good” perturbative fixed point of Kardar—Parisi—Zhang model. Practical calculations of the fixed point coordinates and their regions of stability are calculated to the first order of the (double) expansion in ξ and ε = 2−d (one-loop approximation). Refs 30. Tables 1.